Many clans and families have some degree of Norman blood in them. That goes for several other ethnic backgrounds as well; Norse, Anglo, Saxon, etc.. This is obviously to some limiting degree, which would explain the more predominant Celtic bloodline. Some historians have described Scotland as a melting pot, kind of like NY city. Most of these other cultures contributed in some way to what became the Scottish Identity.

From my perspective, it's just another one of those ever prevalent reasons to be proud of your ancestry.